# The next steps for this Kakuro puzzle

What are the next steps for this Kakuro? I've solved most of it, but there is an area I'm stuck on.

Source: Puzzle Page app

Look at the rightmost column in the part you haven't solved yet:

11 in four has got to be $$1,2,3,5$$ in some order. The top one must be $$2$$ or $$4$$, so now you know it must be $$2$$.

Then the $$5$$ in that column can only be in two places. Trying it in the upper possibility (just below the $$2$$) leads to a contradiction in the column to the left of that (two cells must be $$1$$ and $$3$$, we already have a $$4$$ above, so the remaining cell must be another $$5$$, contradiction). So the $$5$$ is placed, and then everything else should follow easily.

• Thanks for the hints! The first part is just something you have to know, I suppose. I'll know that for next time when I see 11 in four! The second part is even more difficult I think. Can you expand on it a bit further, why after trying the 5 do you deduce that two cells in the column to the left must be 1 and 3? Jun 21 '21 at 21:07
• Alternatively, after determining that the top value in the 27 column is 4, the remaining entries sum to 9, which must be 6+2+1 here, eliminating the bottom 3. Jun 21 '21 at 21:51
• @Kidburla 9 in three with a 5 must be 5+3+1 because 9 - 5 = 4 in two must be 3+1. Jun 21 '21 at 21:54
• @Kidburla A general principle of Kakuro is that the smallest and largest possible sum-in-n always have just one possibility (like $10$ in four must be $1,2,3,4$ while $30$ in four must be $9,8,7,6$), so do the second smallest and second largest ($11$ in four must be $1,2,3,5$ while $29$ in four must be $9,8,7,5$), then the third smallest and third largest have two possibilities ($12$ in four must be $1,2,3,6$ or $1,2,4,5$ while $28$ in four must be $9,8,7,4$ or $9,8,6,5$). Jun 21 '21 at 23:03
• thank you @RobPratt for helping me with the final steps and RandAlThor for your tip about how to spot totals with only one possibility; with these tips I can solve this puzzle and set me in better standing for future Kakuro puzzles! Jun 22 '21 at 8:24